Introduction to Game Theory

General Information
Teacher: 
dr Marcin Łazarz
ECTS: 
4
Number of Hours: 
30
Tuesday 10:15 - 11:45
Preliminary requirements: 

none

Course Description: 

1. Two-person zero-sum games. The concept of the game, the matrix form of the game, strategy, dominant strategy, active and inactive strategy, saddle point, mixed strategy, equalizing strategy, the solution of the game. Minimax theorem. Extensive form: game trees, information sets, games with perfect information, tree pruning technique, competitive decision making.

2. Two-person non-zero-sum games. The concept of the aim in non-zero-sum game. Non-cooperative solutions: Nash equilibria in pure and mixed strategies, prudential and counter-prudential strategies. The Prisoner's Dilemma: Pareto-optimal solutions, games solvable in the strict sense, repeated Prisoner's Dilemma, loyalty, betrayal, trust and suspicion. Communication in the game and the strategic moves: commitments, threats, promises, evolutionarily stable strategies. Cooperation in the game: the concept of the favorite player, the status quo point (negotiations fail), the negotiation set. Axiomatic definition of "fair arbitration" and Nash's theorem. Methods for determining the status quo point (security levels, optimal threat strategies). Applications of Nash arbitration scheme in negotiations between workers and employer, and in the duopoly problem.

3. N-person games. The concept of n-person game, a game in characteristic function form, coalitions in n-person games. Sequential pairwise voting: sincere and sophisticated voting; voting method non-vulnerable to strategic manipulation; defects of democracy. The N-person Prisoner's Dilemma, examples from economics and sport. The Divide-the-Dollar game: individual and collective rationality. A solutions theories for n-person games: theory of stable sets and the Shapley value.

Aims of the course: 

Student:

Identifies in sufficient detail types and techniques of negotiations

Has a complex knowledge abort the relations, connections and associations between different scientific methods in the international relations and other social and political sciences.

Has a deepen knowsledge abort the different types of international forcasting.

Familiarization of students with the basic concepts and techniques of game theory in the context of social science issues. Basic understanding of the issues of game theory, which allows individual reading of more advanced literature of a discipline.

Explains the influence of long-term strategic conditions (related to the issues of survival and development) on the relations between the participants of international relations.

Possess the skill to fluently analyze the international events with the use of scientific instruments and methods.

Is able to use the gained knowledge to lead complex negotiations and use in practice diverse methods of mediation.

Is able to see a new research problem and propose its creative analyze. Can creatively and comprehensively use simulation methods to the multifaceted analysis of different international problems.

Sophistication of students in analytical approach to problems in the field of political science, national security, economics and negotiation theory.

The ability of formalizing a problems and solving them by using the apparatus of game theory.

Can effectively and creatively work and cooperate in group, taking the different roles and thinking and acting innovatively.

Competently refers to the interdisciplinary knowledge in the process of description and explanation of different aspects of the issues of internal and international politics.

Evaluation & Completion: 

Activity, speech, final exam. The grade allocation of each of these components will be:

Activity = 30 %

Speech = 20 %

Final exam = 50 %

Student passes the course if he has the score at least 50 % of all available points.

Basic Literature: 

1) Ph. D. Straffin, Game Theory and Strategy, The Mathematical Association of America, 1996.

2) Joel Watson, Strategy: An Introduction to Game, W. W. Norton & Company, 2002.

Additional Literature: 

1) M.J. Osborne, A. Rubinstein, A course in game theory, The MIT Press, 1994.

2) Fiona Carmichael, A guide to game theory, Financal Times Management, 2004.